Recurrence Relations

  • George E. Martin
Part of the Undergraduate Texts in Mathematics book series (UTM)


A recurrence relation for a sequence {a i }, which usually begins with a 0 or a 1, is a formula that defines a n in terms of a 0, a 1, a 2, a 3,..., a n−1, and n for all n greater than some particular integer k, with the terms a 0, a 1,..., a k called initial conditions or boundary conditions. Together with the initial conditions, the recurrence relation provides a recursive definition for the elements of the sequence. This allows us to compute the unique value of a n for each integer n such that n > k. Many examples follow. We are already familiar with several recurrence relations.


Recurrence Relation Binary Sequence Fibonacci Sequence Catalan Number Quaternary Sequence 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • George E. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

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